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## Homework Statement

Two threads, both having linear density μ

_{1}and μ

_{2}are connected and tensed with tension T.

a) If traveling wave enters onto their junction, find ratios of amplitudes of reflected and input wave, transmitted and input wave, for μ

_{2}/μ

_{1}= 0, 1/4, 1, 4 and infinity

b)

Show that energy flow of input wave is equal to sum of reflected and transmitted wave.

## The Attempt at a Solution

As for part a, it is easy.

We have three waves;

Ψ

_{in}= A cos (ωt - kz)

ψ

_{Tr}= T*A cos (wt -k

_{2}z)

ψ

_{Ref}= R*A cos (wt + kz)

R= (Z

_{1}-Z

_{2})/(Z

_{1}+Z

_{2}), T= 1+ R

Z=(T

_{0}*μ)

^{1/2}

-> R=[(T

_{0}-μ

_{1})

^{1/2}-(T

_{0}-μ

_{2})

^{1/2}]/[(T

_{0}-μ

_{1})

^{1/2}+(T

_{0}-μ

_{2})

^{1/2}]=...=[(1-(μ

_{2}/μ

_{1})

^{1/2}]/[(1+(μ

_{2}/μ

_{1})

^{1/2}].

It is trivial to find those values now.

As for part b)

"The mean energy flux is

*I*, the intensity. For a traveling wave,

quoted from (http://scienceworld.wolfram.com/physics/EnergyFlux.html)

while i assume, U is potential energy.

So basicly, I need to find flux for those three waves, and prove statement.

How to find mean of U as for traveling waves?